'Affordable' is subjective. Needs to be quantified. As also the image quality you look for.

Frankly, birding and budget lenses are mutually exclusive in one's quest for quality images. Unless you plan to shoot mostly in an aviary or the Galapagos Is., even a 400mm lens is often woefully inadequate to obtain a full frame image. Add to that inadequate light in jungle environment, ever present risk of camera shake in telephoto photography, noise at high ISO (to offset this shake) and selecting an 'affordable lens' becomes a complex decision!

If you want quality at lesser price, zooms and lenses slower than f5.6 at the long end are best avoided. If IS is not necessary, go for a Canon 400mm f5.6. Reasonably sharp, light weight, acceptably slow for a telephoto, average price.

With so many suggestions already available, I doubt you will easily arrive at a consensus decision! The best!

Understanding of 'affordable' varies. Care to specify? So many suggestions out here I wonder if they help narrow your search or confuse you! So let me add to the confusion: If you are a primarily tripod based shooter: Canon 400mm f5.6. If not, look for an IS lens - say 70-300 f5.6 DO IS. Or a Sigma/Tamron 300 or 400mm prime lens used. In my view all those 150-500 or 150-600mm lenses offer indifferent quality at the tele end. (Again, image quality is a personal perception. Depends a lot on what you finally plan to do with the picture. )

Gerard, you did not say what sort of bird photos you are wishing to take and the price range or camera, so I this is the lenses I use.
Price-wise, I have very little funds so it would be as cheap as possible and an older second hand lens.
One from the film era would do if you can manually focus without problems. Focal distance of 300mm for close up and 400 to 600mm for further away. The longer the focal length the greater the cost.
My next suggestion is a two times extender, this will double your focal length at the loss of two stops of light.
A 300 mm will become a 600 mm.
Next lens I recommend is a 500mm Mirror lens, the only hassles is you can have only one aperture setting of F8 and some people find their photos a little on the soft side but I have not had this problem, there is no auto focus but they are cheap. My personal lens is a Vivitar 120 - 600 mm with a canon FD mount use with a two times extender it has excellent reach for those long distance shots.
Problems with it is it's weight and no auto focus. I need to use a tripod.
To fit the lens on the camera, I use a cheap FD to EOS adapter, I hope this is some help.

a buddy of mine shoots with the bigma, and his bird pics look really good - he catches a lot of action shots, too.

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Sure, its possible to get pleasing pics with that lens you mention..,.. most modern lenses for that matter! Then again, if one can get good action pics with the relatively slow focussing f5.6 (or is it 6.7?) bigma, imagine what one can get with a Canon 400/2.8 IS or the 500/4 IS?! So the issue to be addressed is not what you get but what you miss on grounds of faster AF and lens speed, better resolution and better IS!

However, even with these fancy $5000+ lenses one may not see much difference or justify the cost from the $500 bigma if all one is going to do is look at the pic on a computer screen in reduced JPG format.

Like I said in my earlier post quality is a subjective matter and essentially a personal interpretation - often a compromise guided often by funds available and muscle to shlep heavy optics.